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The Ramayana is one of Hinduism's greatest epics. Nobody appears to know with certainty when the poem was composed or when the events in it occurred. However, while some scholars claim that the events probably occurred at around the 8th century BCE mark, others claim that it is much, much older.

One section of these other scholars asserts that the events took place circa 7300 BCE (or about 4000 years before the Bronze Age). In the linked article, the author, Dr. P.V. Vartak, even goes as far as narrowing down Rama's (the eponymous hero of the tale) date of birth to 4th December, 7323 BCE. He bases his conclusions on astronomical, meteorological, and cultural data sprinkled throughout the poem. For example,

Mahabharat states that Sage Vishwamitra started counting nakshatras from Shravana (Aadiparva A.71 and Ashwamedha A.44) and a new reference to time measurement thus initiated. According to the old tradition, the first place was assigned to the nakshatra prevelant on the Vernal Equinox. Vishwamitra modified this and started measuring from the nakshatra at the Autumnal Equinox. Sharvan was at this juncture at about 7500 B.C, which is therefore the probable period when Vishwamitra existed and also that of the Ramayanic Era.

Formerly, the year initiated with the Varsha-Rutu (season) and therefore was termed "Varsha". Ramayan shows that the flag was being hoisted to celebrate the new year on Ashwin Paurnima (Kishkindha 16/37, Ayodhya 74/36). Ayodhya 77 mentions that the flags were defaced and damaged due to heat and showers. These descriptions point to the fact that their new year started on the Summer Solstice when heat and rain simultaneously exist. The Summer Solstice fell on Ashwin Full Moon, so the Sun was diagonally opposite at Swati nakshatra. This astral configuration can be calculated to have occured around 7400 B.C.

So it appears that the primary basis for estimating a date is the calendar by Vishwamitra. Other estimates are arrived at relative to this conclusion.

I would like to know if any credence can be given to this claim. Is the supposition about Vishwamitra's "calendar" correct? Are the astronomical aspects of his method reliable? Dr. Vartak claims to have similarly dated the Mahabharata to 5561 BCE.

Both these claims are often sensationalised in reports as providing a scientific evidence of the truth of the events in both epics as well as the time of their occurrence.

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    Calendars change. The monsoons last more than one day. Any attempt to date the Ramayana or the Mahabharata before rather than after the Vedic period is likely to be treated as improbable on linguistic grounds. – Henry Jan 16 '14 at 21:10
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Alf Hiltebeitel, in his review "Introducing the Mahābhārata" (Religious Studies Review 41.4, December 2015), takes an extremely skeptical view of dating the composition. What he is forced to conclude is that there is no evidence either for or against the story existing in any form before 400 BC.

That's pretty much all that can be said about the Mahābhārata from a scientific standpoint. We do not know how old or young the underlying story is. One author claims it can be dated to the 12th century BC (ibid., 166), and Hiltebeitel condemns this as baseless speculation-- it would require 800 years of oral transmission. But there is no evidence against it either. You'd simply have to acknowledge the caveat that many of the details were still being rewritten between 400 BC and 400 AD.

The dates of 7300 BC and 5561 BC are wild speculation, but the general supposition is that an underlying oral narrative does exist (ibid., 155), so the limits of how far back you want to go are defined only by the size of your imagination.

Generally the West doesn't admit the existence of monkey gods who can leap from India to Sri Lanka, so you might have to be courageous with your imagination as well.

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